Answer to Question #89711 in Mechanics | Relativity for Prashraya panta

Question

A copper wire and steel wire of same crossectional area that of length 1m and 2m respectively are connected end to end.A force is applied which stretches their combined length by 1cm.find how much each wire is elongated.

Answer 1

Let the copper wire be 1 with Young's modulus 110 GPa, and the steel wire be 2 with Young's modulus 200 GPa. Their own elongations thus:

$$x_1=\sigma\frac{L_1}{E_1},$$

$$x_2=\sigma\frac{L_2}{E_2}.$$

On the other hand,

$$x_1+x_2=l.$$

Dividing the first two equations one by another, we get an equation for the system of equations with the third one:

$$\frac{x_1}{x_2}=\frac{L_1E_2}{L_2E_1},$$

solve:

$$x_2=\frac{L_2/L_1\cdot lE_1}{E_2+L_2/L_1\cdot E_1}=5.5\cdot10^{-3}\text{ m},$$

$$x_1=l-x_2=4.5\cdot10^{-3}\text{ m}.$$